(CNN) -- Sen. David Vitter broke a week of silence on Monday and, with his wife by his side, denied allegations he had relationships with New Orleans prostitutes.

"I know this has hurt the relationship of trust I've enjoyed with so many of you," Sen. Vitter said Monday.

Media reports surfaced in the past week linking the Louisiana senator to a well-known prostitution case in New Orleans. Vitter attributed those charges to "long-term political enemies" and people seeking money.

Vitter, 46, acknowledged in a statement last Monday that his number was included in the telephone records of an escort service run by Deborah Jeane Palfrey, a woman dubbed by the news media as the "D.C. Madam."

In the statement, Vitter said the incident was "a very serious sin in my past for which I am, of course, completely responsible."

"Several years ago, I asked for and received forgiveness from God and from my wife in confession and marriage counseling."

The phone records were dated before 2004, when Vitter was first elected to the Senate.

"No matter how long ago it was, I know this has hurt the relationship of trust I've enjoyed with so many of you," he said. "I will work everyday to rebuild that trust."

Don't Miss

The family-values Republican also addressed what some critics see as his hypocrisy, saying he's been "trying to live up to the important values we believe" since admitting to his mistakes.

"If continuing to believe in and acknowledge those values causes some to attack me because of my past failure, well, so be it," said Vitter, who does not come up for re-election until 2010.

"I'm not going to answer endless questions about it all over again and again and again and again. That might sell newspapers but it wouldn't serve my family or my constituents well at all," he said.

Vitter's wife, Wendy, told reporters she had forgiven her husband when she learned about the escort service several years ago.

"I made the decision to love him and to recommit to our marriage. To forgive is not always the easy choice, but it was, and is, the right choice for me," she said. "I am proud to be Wendy Vitter."

She also made a plea "as a mother" to the media to give her family some privacy, noting that reporters have been staking out their home and church.

"I would just ask you very respectfully to let us continue our summer, and our lives, as we had planned," she said.

Vitter said he was leaving directly from the hotel for the airport to catch a flight Washington to resume his work in the Senate.

Vitter had been in seclusion since his admission last week. He explained Monday that he and his wife decided it was "very important" for them to spend some time alone with their children.

Palfrey is facing money laundering and racketeering charges stemming from her alleged prostitution operation. She had denied the charges, saying her business was a legitimate, legal escort service.

Vitter is the first lawmaker entangled in the D.C. Madam case, though State Department official Randall Tobias resigned in May after confirming he patronized Palfrey's business.

Larry Flynt's Hustler magazine claimed credit for exposing Vitter's connection to the escort service, saying he came clean only after a journalist working as a paid consultant for the magazine discovered the senator's number on phone records released by Palfrey.E-mail to a friend